The correct option is C The term which involves greatest binomial coefficients is irrational
General term is 6561Cr(76561−r3)11r9.
Terms will be rational if r is a multiple of 9.
∴ r=0,9,18,27,....,6561.
Now 6561=0+(n−1)9⇒n=730
Hence, there are 730 rational terms. The greatest binomial coefficients are 6561C6561−12 and 6561C6561+12
⇒6561C3280 and 6561C3281
Now, 3280 are 3281 are not a multiple of 3; hence, both terms involving greatest binomial coefficients are irrational.